12,792 research outputs found
Chiral Koszul duality
We extend the theory of chiral and factorization algebras, developed for
curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties.
This extension entails the development of the homotopy theory of chiral and
factorization structures, in a sense analogous to Quillen's homotopy theory of
differential graded Lie algebras. We prove the equivalence of
higher-dimensional chiral and factorization algebras by embedding factorization
algebras into a larger category of chiral commutative coalgebras, then
realizing this interrelation as a chiral form of Koszul duality. We apply these
techniques to rederive some fundamental results of \cite{bd} on chiral
enveloping algebras of -Lie algebras
Order Preservation in Limit Algebras
The matrix units of a digraph algebra, A, induce a relation, known as the
diagonal order, on the projections in a masa in the algebra. Normalizing
partial isometries in A act on these projections by conjugation; they are said
to be order preserving when they respect the diagonal order. Order preserving
embeddings, in turn, are those embeddings which carry order preserving
normalizers to order preserving normalizers. This paper studies operator
algebras which are direct limits of finite dimensional algebras with order
preserving embeddings. We give a complete classification of direct limits of
full triangular matrix algebras with order preserving embeddings. We also
investigate the problem of characterizing algebras with order preserving
embeddings.Comment: 43 pages, AMS-TEX v2.
- β¦